$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{4}+3x^{3}-3x^{2}+3x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{5}+4x^{4}\phantom{-;x^n}\phantom{-;x^n}-5x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{5}-x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-x^{4};}\phantom{;}3x^{4}\phantom{-;x^n}\phantom{-;x^n}-5x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-3x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{4}-3x^{3}-;x^n;}-3x^{3}\phantom{-;x^n}-5x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}3x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}3x^{3}+3x^{2}-;x^n-;x^n;}\phantom{;}3x^{2}-5x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-3x^{2}-3x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-3x^{2}-3x\phantom{;}-;x^n-;x^n-;x^n;}-8x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}8x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}8x\phantom{;}+8\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}9\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+3x^{3}-3x^{2}+3x-8+\frac{9}{x+1}$